I was on vacation...
You're right, Max never trusted Chloe. He saw her manipulative side, I think she was less careful around him than around Eddie. She slipped and he probably was watching her, trying to find out more about her. Remember the scene with Max despairing about getting the club ready for the opening, and Eddie helping him out. They were talking about Chloe, and all the questions Max asked Eddie about Chloe's background, Eddie didn't know anything about her!
No wonder he was suspicious of her!
No I don't have a tumblr.